V O L U M5 9E
Eugene J. Kamprath
North Carolina State University
Kenneth J. Frey
Lany P. Wilding
Iowa State University
Texas A&M University
Prepared in cooperation with the
American Society of Agronomy Monograpbs Committee
William T Frankenberger, Jr., Chairman
P. S. Baenziger
David H. Kral
Dennis E. Rolston
Diane E. Storr
Sarah E. Lingle
Jerry M. Bigham
Kenneth J. Moore
Joseph W. Stucki
M. B. Kirkham
Gary A. Peterson
Donald L. Sparks
Department of Plant and Soil Sciences
University of Delaware
San Diego London Boston New York Sydney Tokyo Toronto
This book is printed on acid-free paper. @
Copyright 0 1997 by ACADEMIC PRESS
All Rights Reserved.
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96 97 9 8 9 9 00 01 BB 9 8 7 6 5
John W. Dudley
I. Introduction ..............................................
I1. History ..................................................
I11. Tools of Quantitative Genetics ...............................
Iv. Application of Quantitative Genetics to Plant Breeding . . . . . . . . . . .
V. Future Role of Quantitative Genetics in Plant Breeding . . . . . . . . . . .
Shihe Xu. Guangyao Sheng. and Stephen A . Boyd
Synthesis and Chemical Stability of Organoclays.................
Sorptive Properties of Organoclays ...........................
In Sitzl Modification ........................................
Biodegradation of Contaminants in Modified Soils ...............
SHOOT APEX: A &VIEW
Gregory S. McMaster
I. Introduction ..............................................
I1. General Patterns of Grass Shoot Apex Development .............
I11. Morphological Nomenclatures ...............................
Iv. Shoot Apex Developmental Sequence .........................
V Conclusion ...............................................
I . Introduction ..............................................
11. Methods Used in Micromorphology ..........................
I11. Soil Structure in Relation to Land Use .........................
IV. Conclusions and Future Research Needs .......................
Matt A. Sanderson. David W. Stair. and Mark A. Hussey
I. htroduction ..............................................
I1. Water Deficit .............................................
I11. Defoliation Stress..........................................
Low Light ...............................................
v. Nutrient Stress............................................
VI. Low-Temperature Stress ....................................
VII. Salt Stress ................................................
VIII. Plant Breeding for Abiotic Stress Tolerance .....................
A COTTON EXAMPLE
K. Raja Reddy. Harry F. Hodges. and James M . McKinion
I. Introduction ..............................................
I1. Phen o1ogy ...............................................
111. Growth of Individual Organs ................................
Iv. Partitioning Biomass .......................................
v High-Temperature Effects on Fruiting Structures . . . . . . . . . . . . . . . .
VI. Nitrogen-Deficit Effects ....................................
VII . Water-Deficit Effects.......................................
VIII. Model Development .......................................
IX. Model Calibration and Validation .............................
X . Model Applications and Bridging Technologies . . . . . . . . . . . . . . . . . .
XI . Summary and Conclusions ..................................
A. Edward Johnston
The Rothamsted Experiments ...............................
The Agricultural Value of Long-Term Experiments . . . . . . . . . . . . . .
Ecological Research and Long-Term Experiments . . . . . . . . . . . . . . .
Long-Term Experiments and Environmental Concerns . . . . . . . . . . .
VI. The Need for Long-Term Experiments ........................
VII. Approaches to New Long-Term Experiments . . . . . . . . . . . . . . . . . . .
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Numbers in parentheses indicate the pages on which the authors’contributions begin.
STEPHEN A. BOYD (2 S), Department of Crop and Soil Sciences, Michigan State
University,East Lansing, Michigan 48824
JOHN W. DUDLEY (I), Department o f Crop Sciences, University of Illinois at
Urbana-Champaign, Urbana,Illinois 61 801
HARRY F. HODGES (229, Department of Plant and Soil Sciences, Mississippi
State University, Mississippi State, Mississippi 39762
MARK A. HUSSEY (17 I), Department of Soil and Crop Sciences, Texas A&M
University,College Station, Texas 77843
A. EDWARD JOHNSTON (291), MCR Rothamsted, Harpenden, Herts A L 5
ZJQ, United Kingdom
JAMES M. MCKINION (226), USDA-ARS Crop Simulation Research Unit,
Mississippi State, Mississippi 39762
GREGORY S. MCMASTER (63), USDA-ARS, Great Plains Systm Research,
Fort Collins,Colorado 80522
RIENK MIEDEMA (1 19), Department of Soil Science and Geology, Wageningen
Agricultural University,6700 AA Wageningen,The Netherlands
K. RAJA REDDY (22S), Department of Plant and Soil Sciences, Mississippi State
University,Mississippi State, Mississippi 39762
MATT A. SANDERSON (17 l), Texas A&M UniversityAgricllltural, Research
and Extension Centq Stephenville, Texas 76401
GUANGYAO SHENG (2 S), Department of Crop and Soil Sciences, Michigan
State University, East Lansing, Michigan 48824
DAVID W. STAIR (1 7 l), Department ofsoil and Crop Sciences, TexasA&M University, College Station, Texas 77843
SHIHE XU (2 5 ) , Health and Environmental Sciences, Dow Corning Corporation,
Midland, Michigan 48640
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Volume 59 contains seven state-of-theart reviews of various crop and soil sciences
topics. The first chapter presents an overview of quantitative genetics and plant
breeding, including historical aspects, the tools of quantitative genetics, the application of quantitative genetics to plant breeding, and the future role and importance of quantitative genetics in plant breeding. The second chapter reviews the
use of organoclays in pollution abatement. Topics discussed include synthesis,
chemical stability, sorptive properties of organoclays, in siru soil modification, and
biodegradationof contaminants in modified soils. The third chapter covers the phenology, development, and growth of the wheat shoot apex, including general patterns of grass shoot apex development, morphological nomenclatures, and shoot
apex developmental sequences. The fourth chapter applies micromorphology to
agronomic scenarios. The discussion includes methods that are used in micromorphology and soil structure in relation to land use. The fifth chapter discusses
the physiological and morphological responses of perennial forages to stresses, including water deficits, defoliation, nutrients, low temperature, and salt. The sixth
chapter is a comprehensive review of crop modeling and applications, with cotton
as the crop of interest. Discussions on phenology, growth of individual organs, partitioning biomass, high-temperature effects of fruiting structures,nitrogen and water deficit effects, and model development,calibration, validation, and applications
are included. The seventh chapter is a historically rich overview of the importance
of long-term field experiments in agricultural, ecological, and environmental research.
I appreciate the first-rate reviews of the contributors.
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John W. Dudley
Department of Crop Sciences
University of Illinois
Urbana. Illinois 61801
A. Plant Breeding
B. Quantitative Genetics
C. Use of Quantitative Genetics in Plant Breeding
111. Tools of Quantitative Genetics
A. Description of Genetic Variation
B. Description of Environmental Variation
C. Predicted Gain Equation
D. Correlated Response Equation
E. Multiple Trait Selection Index
E Molecular Markers
G. Generation Mean Analysis
W. Application of Quantitative Genetics to Plant Breeding
A. Choice of Parents
B. Selection during Inbreeding
C. Recurrent Selection
D. Marker-Assisted Selection
V. Future Role of Quantitative Genetics in Plant Breeding
The objective of this chapter is to review the relationship between quantitative
genetics and plant breeding from a plant breeding perspective. Plant breeding is
the science and art of genetic improvement of crop plants. Quantitative genetics is
the study of genetic control of traits that show a continuous distribution in segregating generations. Quantitative genetics is concerned with the inheritance of
those differences between individuals that are of degree rather than kind, quanti1
A d v m r s in A p n n m y . Volume 79
Copyright 0 1YY7 by Academic Press, Inc. All rights of reproduction in any form reserved.
JOHN W. DUDLEY
tative rather than qualitative (Falconer, 1989). Where do these disciplines intersect? At one extreme, Kempthorne (1977) defined plant breeding as applied quantitative genetics. Simmonds (1984) on the other hand, considered biometrical genetics “to have helped to interpret what has already been done and to point
questions, especially about the all important matter of response to selection, but to
have had little impact on the actual practice of breeding.” Baker (1984) provided
an intermediate view when he suggested an understanding of quantitative genetic
principles is critical to the design of efficient breeding programs. In this review,
Baker’s viewpoint will be followed. Because many of the most important traits
with which breeders work are inherited quantitatively, quantitative genetics must
be of concern to breeders.
Plant breeding started with primitive people saving seed to plant in succeeding
years. In the process, most of our major crops, such as maize (&a mays L.), wheat
(Triticurn aestivum L.), barley (Hordeurn vulgare L.), and many others, were domesticated. Although there is a tendency to equate the beginnings of plant breeding with the rediscovery of Mendel’s laws, major plant breeding discoveries were
made prior to 1900. For example, mass selection for sucrose concentration in the
beet root began in 1786 and was continued until 1830. The first beet sugar factory was erected in 1802 (Smith, 1987). Thus, planned, directed plant breeding efforts resulted in a cultivar that allowed development of a new industry 100 years
before the rediscovery of Mendel’s laws. The basic principles underlying maize
breeding, i.e., that inbreeding reduces vigor, cross-breeding increases vigor, hybrids could be produced by detasseling one parent, and that hybridization needed
to be done each generation if vigor was to be maintained, were known prior to 1900
With the rediscovery of Mendel’s laws, genetic principles began to be applied
to plant breeding. Smith (1966) traces the developments from 1901 to 1965, including developments in statistical theory that had important implications for plant
breeders. The development of hybrid corn and the principles leading to it have been
reviewed extensively (Crabb, 1947; Hayes, 1963; Wallace and Brown, 1956) and
will not be reviewed in detail here.
Because most of the traits of economic importance are under quantitative genetic control, quantitative genetics became an important contributor to plant breeding theory.
QUANTITATIVE GENETICS AND PLANT BREEDING
Selection for quantitative traits began with the first person to select for productivity of the plants from which seeds were saved for the next generation. However, the origins of quantitative genetics can be traced to Darwin’s concept of natural selection (Griffing, 1994).Early statistical concepts, such as regression (Galton,
1889) and use of correlation and multiple regression to describe relationships
among relatives (Pearson, 1894),were developed prior to rediscovery of Mendel’s
laws. Griffing (1 994) listed the demonstration of the environmental nature of variation among plants within lines and the genetic nature of variation among lines
(Johannsen, 1903, 1909) along with the establishment of the multiple factor hypothesis for inheritance of quantitative traits by the experimental studies of Nilsson-Ehle (1909) and East (1910) as keys to demystification of inheritance of quantitative traits. On the theoretical side, the development of the Hardy-Weinberg
equilibrium concept demonstrated a mechanism for maintenance of genetic variability in populations. The study that formed the basis for most of the theoretical
quantitative genetics work to follow was that of Fisher (1918), which showed that
biometric results (involving correlations among relatives) could be interpreted in
terms of Mendelian inheritance. Griffing (1994) traces the history of quantitative
genetics in detail. A few additional milestones that he identifies include the work
of Cockerham (1954) and Kempthorne (1954) in partitioning epistatic variation
and the contributions of Kempthorne (1957) in bringing together and interpreting
in a common statistical genetic language the diverse concepts of prominent statistical geneticists.
As areas of plant breeding in which they were important are considered, other
important steps in the history of quantitative genetics will be reviewed.
C. USEOF QUANTITATIVE
Quantitative genetic principles apply to almost any area of plant breeding.
Breeders recognize the need for more extensive testing for traits of low heritability than for traits of high heritability. They cross good X good, understanding the
principle that lines with similar means are likely to differ at fewer loci than dissimilar lines and thus transgressive segregants are more likely to occur. However,
the formal use of such quantitativegenetic techniques as estimation of genetic variances and prediction of genetic gain is rare in most plant breeding programs. In
this review, each of the steps in a plant breeding program will be examined and the
utility of quantitative genetic techniques considered. However, before describing
the use of these techniques in plant breeding, a brief description of the tools available from quantitative genetics is provided.
JOHN W. DUDLEY
III. TOOLS OF QUANTITATIVE GENETICS
Because quantitative traits are those for which the effects of genotype and environment cannot be readily distinguished,a major contribution of quantitative genetic theory was to provide methods for separating genetic effects from environmental effects. As a first step, genetic expectations of means and variances were
Based on the work of Fisher (1918) and the elaborations by Cockerham (1954)
and Kempthorne (I 954), procedures for describing genetic variation in a population were developed. These procedures are based on first describing within-locus
variation in terms of average effect of substitutionof an allele and deviations from
that average effect. Variation associated with the average effect of substitution is
called additive genetic variance and variance associated with deviations is called
dominance genetic variance (see Falconer, 1989, for details). Variance associated
with interaction among alleles at different loci is termed epistatic genetic variance
and can be subdivided into additive X additive, additive X dominance, and dominance X dominance variance when two loci are involved. When additional loci
are involved, higher-order interactions can be described. Genetic variance components can be estimated from covariances between relatives as described by
Cockerham ( 1963).
The general procedure for estimating genetic components of variance is to devise a mating design that will estimate covariances between relatives (such as the
covariance of full-sibs or half-sibs). The mating design is then grown in an environmental design. The environmental design includes the choice of environments
(usually locations and years) and environmentalstresses (such as plant population,
irrigation or lack thereof, fertility levels, etc.) as well as the experimental design
(such as a randomized complete block, incomplete block, or other type of design).
From the appropriate analysis of variance, design components of variance are estimated and equated to covariances between relatives. Estimates of covariances
between relatives are then equated to expected genetic variance components and
genetic variances are estimated (Cockerham, 1963). Such estimates have limitations. Assumptions usually include linkage equilibrium in the population from
which the parents of the mating design were obtained and negligible higher-order
epistatic effects. The epistatic effects assumed negligible vary with the mating design, e.g., if only one covariance between relatives, such as half-sibs, is estimated, then all epistatic effects are assumed negligible if the covariance of half-sibs
is assumed to be an estimate of a portion of the additive genetic variance.
QUANTITATIVE GENETICS AND PLANT BREEDING
As will be discussed later, estimates of genetic variance components can be used
to predict gain from selection (thus allowing comparisons among breeding methods), determine degree of dominance for genes controlling quantitative traits, and
compare heritability of different traits.
For any plant breeding program to be successful, the environments in which the
cultivars being developed are to be grown must be defined. Selection is then concentrated on developing cultivars that can take maximum advantage of that environment. The one factor that dictates extensive, expensive testing of genotypes in
a plant breeding program is the existence of genotype-environment interaction
Four aspects of GXE need to be considered. First, does GXE exist? Comstock
and Moll (1963) described in detail methods of estimating GXE components of
variance and detecting the existence of GXE. Second, if GXE does exist, are genotypes ranked the same in different environments? If GXE effects are significant
because of differences in magnitude of differences between genotypes in different
environments (non-crossover interaction) rather than differences in ranking of
genotypes between environments (crossover interactions), then the GXE effects
are of little consequence to the breeder. An extensive discussion of methods of
measuring the importance of crossover and non-crossover interaction effects is
given by Baker (1988). Third, which genotypes respond most favorably to changes
in environment? Regression of performance of a genotype on the average performance of a set of genotypes in an environment (Finlay and Wilkinson, 1963; Eberhart and Russell, 1966) has been used to identify genotypes that respond favorably
to environmentsor that do not respond to increased environmentalinputs. Detailed
discussion is found in Lin et al. ( 1 986) and Romagosa and Fox (1993). Fourth,
measures of GXE have been used to define geographic regions with similar environments in order to identify areas in which test sites should be located (Ouyang
et al., 1995). Clustering procedures described by Ouyang et al., emphasize detecting crossover interaction and allow computation of distances between environments for unbalanced or missing data.
Although the procedures used for dealing with GXE are primarily statistical, the
traits being considered are quantitative and the genetic constitution of the entries
being evaluated affects the results. For example, Eberhart and Russell (1969) determined single crosses were, on average, less stable than double crosses. However, they found individual single crosses that were as stable as most double
crosses. The removal of GXE variance from estimates of genetic variance is an integral part of any attempt to estimate genetic variances for prediction of gain from
selection. Choice of environments for such a study is also critical. A symposium
JOHN W. DUDLEY
volume edited by Kang (1990) provides a detailed look at the interrelationshipsof
GXE and plant breeding.
One of the major contributions of quantitative genetics to plant breeding was
the development of an equation for predicting gain from selection. Griffing (1994)
reviews the historical developmentof the prediction equation beginning with Fisher’s ( I9 18) consideration of the ratios of U;/CT~ and
as measuring the relative importance of additive genetic and dominance contributions to correlation
analysis. Wright ( 1 92 1) originated the concept of broad-sense heritability and
Lush (1935), using Fisher’s least squares gene model, partitioned the hereditary
contribution into additive and nonadditive portions. From this work came the concept of the ratio of ui/ug as a measure of heritability in the narrow sense. A detailed discussion of the estimation of heritability is given by Nyquist (1991).
In its simplest form, the predicted gain equation has been expressed as R =
ia,@r,, which can be recast as R = ihiu,, where R is response to selection, i is the
standardized selection differential, and h i is narrow-sense heritability. This expression assumes selection based on phenotype of individuals and recombination
of selected individuals. However, there are a number of factors in plant breeding
programs that complicate this simple expression. Hallauer and Miranda ( 1988),
Empig et al. (1972), and Nyquist (1 99 1) explore these factors in detail. Because
selection in plant breeding programs is based on progenies and these progenies
vary in the types and proportions of genetic variance expressed, the appropriate
types of genetic variance to be included in the numerator of the selection equation
vary. In addition, the estimate of phenotypic variance to be included in the denominator varies with the experimental and environmental designs used. The basis for comparison of results from the prediction equation may also vary. For example, selection procedures may be compared on either a per year or a per cycle
basis. Finally, the choice of whether recombination is such that selection is based
on both the male and female parents of the next generation or only on one sex will
play a role in progress from selection.
Given the factors mentioned in the preceding paragraph, a generalized prediction equation for gain per year can be written as follows (Empig et al., 1972):
R = cisi/yu,,
where c is a pollen control factor (iif selection is after pollination, 1 if selection
is prior to pollination, and 2 if selfed progenies are recombined), y is the number
of years per cycle, i is the selection differential expressed as number of up,si is
the appropriate genetic variance for the type of selection being practiced, and a,,
is the appropriate phenotypic standard deviation for the progenies being evaluat-
QUANTITATIVEGENETICS AND PLANT BREEDING
ed in the selection program. If comparisons on a per cycle basis are desired, then
y can be set as 1 for all types of selection being compared. This equation is critical for comparing selection procedures. Examples of its use are given by Hallauer
and Miranda (1 988) and Fehr (1987).
When selection is applied by plant breeders, changes are likely to occur, not only
in the trait for which selection is being practiced but in other traits as well (correlated response). The extent of correlated response is a function of the heritabilities
of the primary and correlated traits, as well as the genetic correlation between the
traits. Falconer ( 1989) presents the correlated response equation as
CRY = ih,$iyrAupy,
where CRY is the correlated response in trait Y when selection is based on trait X,
i is the standardized selection differential for X , h, and h,, are the square roots of
heritability of traits X and Y, respectively, rA is the additive genetic correlation between X and Y and uPyis the appropriate phenotypic standard deviation for I:Multiplying CRY by c/y generalizes the equation to a form corresponding to Eq. (1).
Hallauer and Miranda (1 988) describe calculation of genetic correlations. Equation (2) becomes important not only in determining the type of correlated response
that may occur under selection but also in determining effectivenessof indirect selection. If rAhx > hy then indirect selection for X will be more effective than direct selection for Y, all other factors being equal. If, in addition, selection for X allows progress in an environment where Y cannot be measured, as may be true for
marker-assisted selection, then additional benefits accrue from indirect selection.
The cultivars arising from plant breeding programs must satisfy a number of criteria to be useful. For example, a high yielding cultivar susceptible to a prevalent
disease would be of little use to a grower, Thus, plant breeders must select for a
number of traits. Three general procedures-tandem selection, independent
culling levels, and index selection-have been used to approach the question of
simultaneous improvement of a population for multiple traits (Falconer, 1989). A
number of forms of the equation for gain from index selection for multiple traits
are available. Smith (1936) was the first to present the concept of index selection.
Smith presented an index of the form:
I = b,X,
+ b2X2 + . .
JOHN W. DUDLEY
where I is an index of merit of an individual and 6, . . . 6, are weights assigned to
phenotypic trait measurements represented as X,. . .X,. The b values are the product of the inverse of the phenotypic variance-covariance matrix, the genotypic
variance-covariance matrix, and a vector of economic weights, A number of variations of this index, most changing the manner of computing the b values, have
been developed.These include the base index of Williams (1962), the desired gain
index of Pesek and Baker (1969), and retrospective indexes proposed by Johnson
et al. (1988) and Bemardo (1991). The emphasis in the retrospective index developments is on quantifyingthe knowledge experienced breeders have obtained. Although breeders may not use a formal selection index in making selections, every
breeder either consciously or unconsciously assigns weights to different traits
when making selections.
Although molecular markers are not a direct product of quantitative genetics,
the explosion of interest in their use in plants is in large part because of the implications they have for helping solve problems that are common to quantitative genetics and plant breeding. The use of markers as a potential aid in selection dates
back to Sax (1923) who found seed color related to seed size in beans. Stuber and
Edwards (1986) pioneered the use of molecular markers in plant breeding with
work based on isozymes. Stuber (1992) reviewed this work. The use of markers
for selection in plant breeding programs is the application of a form of indirect selection. The use of markers to manipulate genes was reviewed in detail by Dudley
(1993). Lee (1995) gave a comprehensive review of use of molecular markers in
plant breeding. The availability of molecular markers provides an additional dimension to the use of quantitative genetics in plant breeding. Potential applications of molecular markers include marker-assisted selection, identification of the
number of genes controlling quantitative traits, grouping germ plasm into related
groups, selection of parents, and marker-assisted backcrossing.
The broad area of generation mean analysis is summarized by Mather and Jinks
(1982). In essence, the procedure expresses the means of generations derived from
the cross between homozygous lines in genetic terms. The generation means are
then analyzed to estimate additive, dominance, and epistatic effects. The reference
population is either the F, mean or the mean of homozygous lines resulting from
selfing the F,. Procedures for estimating the number of effective factors affecting
a particular trait in the cross being studied are provided. One of the major limita-
QUANTITATIVE GENETICS AND PLANT BREEDING
tions of the procedure is the assumption that, for the trait being studied, one parent contains all the favorable alleles and the other all the unfavorable alleles at segregating loci. The procedure has found a great deal of use in studying genetics of
disease resistance (Campbell and White, 1995; Carson and Hooker, 1981; Moll et
al., 1963). An advantage cited by those using it is that the progenies used to determine segregation for single genes can also be used for generation mean analysis. In addition, means are less variable than variances.
Iv. APPLICATION OF QUANTITATIVE GENETICS
TO PLAN" BREEDING
Plant breeding consists of selection of parents, crossing those parents to create
genetic variability, selection of elite types, and synthesis of a stable cultivar from
the elite selections. Quantitative genetic principles play a role at each of these
stages. In this section, the role of quantitative genetics in each of these stages of
the plant breeding process is considered.
The choice of parental germ plasm with which to begin a breeding program is
the most important decision a breeder makes. However, it is only relatively recently that quantitative genetic theory has been applied to this question.
1. Self-Pollinated Crops
Discussion of choice of parents in self-pollinatedcrops will be in the context of
selecting parents from which selfed lines will be derived using a pedigree system,
single-seed descent, or some other method of deriving inbreds. In self-pollinated
species, these lines usually are evaluated for their per se performance. In crosspollinated species, in which hybrids are the end product, similar breeding procedures are used with the exception that the end product will be a hybrid. Thus, the
criterion for selection is combining ability of some form rather than line per se performance.
The objective when choosing parents is to maximize the probability of generating new lines that will perform better than the best pure line currently in use. The
parents chosen should generate a population for selection that will meet the criterion of usefulness described by Schnell (1983) as discussed in Lamkey et al.
(1995). Usefulness of a segregating population was described by Schnell as the
mean of the upper a% of the distribution expected from the population. Mathe-
JOHN W. DUDLEY
matically, U(a)= Y 2 AG(a), where U(a)is usefulness, Y is the mean of the unselected population, and AG(a)is gain from selection. This statistic takes into account both the mean and the genetic variability, thus emphasizing a basic axiom
in plant breeding: Both a high mean and adequate genetic variability are needed
to produce a superior cultivar.
Another basic principle of plant breeding is to cross good x good to obtain something better. The quantitative genetic basis for this axiom was demonstrated by
Bailey and Comstock ( 1976).Their results demonstrated,based on probability theory and computer simulation results, the importance of each parent contributing
favorable alleles from nearly equal numbers of loci that are segregating in the
cross. Their results can be illustrated by considering 60 loci segregating in an F,.
With no selection, the probability of a line having >39 loci fixed at homozygosity
would be 0.0067, whereas the probability of a line having greater than 30 loci fixed
would be 0.4487. Thus, if each parent line contributed favorable alleles at 30 loci,
the probability of obtaining a line with a higher number of loci fixed with favorable alleles than the better parent would be relatively large. However, if one parent contributed favorable alleles at 40 loci and the other at only 20, the probability of obtaining a new line better than the better parent would be small.
Dudley (1 982) suggested backcrossing one or more times to the superior parent
if one parent was much superior to the other. The number of backcrosses needed depended on the relative number of favorable alleles coming from each parent-the
greater the divergence between parents, the more backcrossing would be needed.
Given the criteria of a high mean and relatively high genetic variance, what tools
are available to a breeder to identify parents that will provide segregating generations with these characteristics? Baker (1984) reviewed this question in light of a
paper by Busch et al. (1974) who evaluated F4 and F, bulk populations, random
F,-derived F5 and F, lines, and midparent values as predictors of cross performance. Baker suggests any of these methods should be useful predictors of the
mean performance of lines from an F, with the caution that midparent values might
be the weakest of the methods. Toledo (1992) found use of the midparent value
and the inverse of Malecot’s coefficient of parentage to be effective in selecting
crosses that would produce superior lines in soybeans (Glycine m a L., Merrill).
Panter and Allen (1995) suggested using best linear unbiased prediction (BLUP)
methods to predict the midparent value of soybean crosses. BLUP methods take
into consideration the performance of lines related to the line for which performance is being predicted. They concluded BLUP had advantages over least
squares estimates of midparent values. They found a correlation of -0.47 between
coefficient of parentage and genetic variance in progeny. Based on these results,
they suggested that an effective method of choosing parents would be to identify
pairs of lines with high midparent values estimated from BLUP and to select
among such pairs those which were the most genetically diverse based on the ge-
QUANTITATrVE GENETICS AND PLANT BREEDING
netic relationship matrix. Their suggestion is supported by the results of Toledo
(1992). With the availability of genetic markers, degree of relationship between
lines can be established from molecular marker data (Lee, 1995). This provides an
alternative method of determining relatedness when pedigree information is unavailable or of uncertain accuracy.
2. Cross-Pollinated Crops (Hybrid Cultivars)
For development of hybrid cultivars, there are two aspects to the choice of
parents: (i) choice of parents to cross to form base populations for selfing, and
(ii) choice of parents to form a cultivar for use by farmers. These two aspects will
be addressed separately.
a. Choice of Parents to Form Base Populations
Conceptually, the problem of developing improved inbreds for use in hybrids is
one of adding favorable alleles from a donor source to an elite inbred without materially reducing the frequency of favorable alleles already present in the elite inbred (Dudley, 1982). The basic question in choosing parents is identification of
those lines or populations that contain favorable alleles not present in a hybrid being improved. Dudley ( 1984a) framed the following questions relative to choice
of parents for a hybrid corn breeding program: Which hybrid should be improved?
Which lines should be chosen as donors to improve the target hybrid? Which parent of the target hybrid should be improved? Should selfing begin in the F, or
should backcrossing be used prior to selfing?
Procedures for answering these questions were developed based on the concept
of classes of loci. This concept was first explored in Dudley (1982). The basic concept assumes that for any pair of lines the loci at which the lines differ for a given
trait can be divided into two classes: those loci for which P, contains favorable alleles and P, does not and those for which P, contains favorable alleles and P, does
not. When a donor inbred is considered, eight classes of loci exist as illustrated in
Table 1. Of critical interest is the class of loci for which the donor contains favorable alleles and both parents of the target hybrid have unfavorable alleles. Using
this concept, methods of identifying donors with the greatest numbers of such loci
were devised for cases in which the donor was an inbred or a population (Dudley,
1984b,c, 1987a,b). Modifications of these methods were proposed by Gerloff and
Smith (1988), Bernard0 (1990a,b), and Metz (1994). Evidence for their effectiveness in selecting superior parents and identifying heterotic relationships was presented by Dudley (1988), Misevic (1989), Zanoni and Dudley (1989), Pfarr and
Lamkey (1992), and Hogan and Dudley (1991). These methods are beginning to
be used in commercial breeding programs in corn and sorghum [Sorghum bicolor
JOHN W. DUDLEY
Genotypes for the Classes of Loci Possible for
the Parents of a Hybrid to Improve (P, and Pz)
and a Donor Inbred (PJ
Class of loci
a + + , The line is homozygous for the dominant favorable allele; - -, homozygous for the recessive unfavorable allele.
b. Choice of Parents of a Hybrid Cultivar
Choice of parents to produce a cultivar directly is usually the result of extensive
testing of a number of combinations of potential parents. One of the major problems facing breeders is reducing the number of possible hybrids to be tested to a
reasonable number. In general, breeders work with heterotic groups and crosses
likely to be successful as cultivars are usually between inbreds from different heterotic groups (Hallauereral., 1988). However, even if breeding is restricted to two
heterotic groups, thousands of potential hybrids are possible.
Bernardo (1994) proposed applying BLUP to this problem. In this procedure,
information on hybrid performance of a subset of lines is combined with information on genetic relationship between the lines tested and an untested set of lines
to predict the performance of untested hybrids. This procedure has been widely
used in dairy cattle breeding (Henderson, 1988). Bernardo (1994), using a limited
number of hybrids, found correlations between observed and predicted performance ranging from 0.65 to 0.80. He compared RFLP-based estimates of relationship with pedigree-based estimates and found higher correlations for the
RFLP-based estimates. In a study (Bernardo, 1996) involving 600 inbreds and
4099 tested single crosses, correlations between predicted and observed yields
ranged from 0.426 to 0.762. Bernardo concluded BLUP was useful for routine
identification of single crosses prior to testing.